We prove a structure theorem for topologically conservative real skew product extensions of distal minimal compact metric Z-flows. The main result states that every such extension can be represented by a perturbation of a Rokhlin skew product. Moreover, we give certain counterexamples to point out that all components of the construction are in fact inevitable.
Let f : Q n i=1 X i −→ Z be a measurable function defined on the product of finitely many standard probability spaces (X i , B i , µ i), 1 ≤ i ≤ n, and which takes values in any standard Borel space Z. We consider the Borel group of all n-tuples (g 1 ,. .. , gn) of measure preserving automorphisms of the respective spaces (X i , B i , µ i) such that f (g 1 x 1 ,. .. , gnxn) = f (x 1 ,. .. , xn) almost everywhere and prove that this group is compact provided that we factorise out its 'trivial' symmetries. As a consequence we are able to characterise all such groups which result in such a way. This problem appears with the question of classifying measurable functions in several variables (which has been solved in the paper [Ve1]) but is interesting in itself.
With the rise of cloud computing new ways to secure outsourced data have to be devised. Traditional approaches like simply encrypting all data before it is transferred only partially alleviate this problem. Searchable Encryption (SE) schemes enable the cloud provider to search for user supplied strings in the encrypted documents, while neither learning anything about the content of the documents nor about the search terms. Currently there are many different SE schemes defined in the literature, with their number steadily growing. But experimental results of real world performance, or direct comparisons between different schemes, are severely lacking. In this work we propose a simple Java client-server framework to efficiently implement different SE algorithms and compare their efficiency in practice. In addition, we demonstrate the possibilities of such a framework by implementing two different existing SE schemes from slightly different domains and compare their behavior in a real-world setting.
We resume the results from [Ver02a] on the classification of measurable functions in several variables, with some minor corrections of purely technical nature, and give a partial solution to the characterization problem of so-called matrix distributions, which are the metric invariants of measurable functions introduced in [Ver02a]. The characterization of these invariants, considered as S N × S N -invariant, ergodic measures on the space of matrices is closely related to Aldous' and Hoover's representation of row-and column-exchangable distributions [Ald81, Ho82], but not in such an obvious way as was initially expected in [Ver02a].
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